Implementation of the iterative PDFT algorithm with applications to inverse synthetic aperture radar imaging

Many imaging methods are based on inverting scattered field data. Depending on the wavelength of the radiation with respect to the scale of the scattering inhomogeneities, this inverse problem is more or less straightforward. In the small wavelength limit beam attenuation and projection tomographic algorithms are appropriate. When the wavelength approaches the size of the inhomogeneities, scattering, especially strong scattering makes the problem intractable. One can relate the scattered field to a secondary source by a Fourier transformation. The secondary source is easily related to the scattering distribution itself in a weakly scattering approximation. A very important problem arises from inverting Fourier data acquired from limited numbers of noisy measurement samples. In this thesis we focus on addressing this issue in order to improve the estimate of the image (or Secondary source). If measured data filled the entire Fourier space of the scatterer there would be no problem but with limited data the image will be convolved with the envelope of the sampling space. Improvements in image quality are possible using a spectral estimation method known as the PDFT which uses the available data and prior knowledge about the image. Previous work based on the PDFT has been very successful in recovering images with improved fidelity and resolution. However this was clone only for objects of compact support in homogeneous backgrounds. Also, the implementation of' the PDFT algorithm was computationally demanding with large data sets. Our original contribution to this problem is to extend the FDFT to recover images of objects in cluttered backgrounds and evaluate an iterative algorithms that speeds up the computation of the PDFT estimate.; We illustrate the use of appropriately structured prior in the PDFT to alleviate poor image quality when clutter is present. For disconnected prior a separate prior has to be constructed for each separate part of the object. The problem of a wide area clutter with strong intensity is shown to be well addressed by a prior that is constructed as a smooth window function.; For very large data sets, a discrete PDFT (DPDFT) algorithm is presented and implemented by incorporating the iterative algebraic reconstruction technique (ART) into the PDFT algorithm. Critical issues concerning the rate and error of the convergence are investigated. By careful arrangement of the order in which the data are processed and a good selection of relaxation or regularization, the DPDFT can reconstruct a high-quality image with excellent computational efficiency.; In order to illustrate the potential of the algorithm developed as part of this investigation the imaging performance is demonstrated from simulated and measured data sets.